Abstract

We present a simple theory explaining the extraordinary features of high-contrast optical gratings in the near-wavelength regime, particularly the very broadband high reflectivity (>99%) and the ultra-high quality factor resonances (Q>107). We present, for the first time, an intuitive explanation for both features using a simple phase selection rule, and reveal the anti-crossing and crossing effects between the grating modes. Our analytical results agree well with simulations and the experimental data obtained from vertical cavity surface emitting lasers incorporating a high contrast grating as top reflector.

© 2012 OSA

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    [CrossRef] [PubMed]
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  17. C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
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    [CrossRef] [PubMed]
  19. V. Karagodsky, B. Pesala, C. Chase, W. Hofmann, F. Koyama, and C. J. Chang-Hasnain, “Monolithically integrated multi-wavelength VCSEL arrays using high-contrast gratings,” Opt. Express 18(2), 694–699 (2010).
    [CrossRef] [PubMed]
  20. F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18(12), 12606–12614 (2010).
    [CrossRef] [PubMed]
  21. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
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  28. V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
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    [CrossRef] [PubMed]

2012 (1)

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

2011 (1)

2010 (6)

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010).
[CrossRef] [PubMed]

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

V. Karagodsky, B. Pesala, C. Chase, W. Hofmann, F. Koyama, and C. J. Chang-Hasnain, “Monolithically integrated multi-wavelength VCSEL arrays using high-contrast gratings,” Opt. Express 18(2), 694–699 (2010).
[CrossRef] [PubMed]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18(12), 12606–12614 (2010).
[CrossRef] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

2009 (2)

2008 (3)

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high contrast grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[CrossRef] [PubMed]

2007 (2)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Optical modulation using anti-crossing between paired amplitude and phase resonators,” Opt. Express 15(25), 17264–17272 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (3)

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

2002 (1)

1999 (1)

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

1998 (2)

S. Astilean, P. Lalanne, P. Chavel, E. Cambril, and H. Launois, “High-efficiency subwavelength diffractive element patterned in a high-refractive-index material for 633 nm,” Opt. Lett. 23(7), 552–554 (1998).
[CrossRef] [PubMed]

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

1997 (1)

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

1993 (1)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40(4), 553–573 (1993).
[CrossRef]

1992 (2)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[CrossRef] [PubMed]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

1989 (1)

1981 (1)

Ager, J. W.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Arakawa, Y.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[CrossRef] [PubMed]

Astilean, S.

Baets, R.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Bakir, B. B.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Bartelt, H.

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Bolten, J.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Boons, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Britzger, M.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Brückner, F.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Burmeister, O.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Caekebeke, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Cambril, E.

Chang-Hasnain, C. J.

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[CrossRef] [PubMed]

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010).
[CrossRef] [PubMed]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18(12), 12606–12614 (2010).
[CrossRef] [PubMed]

V. Karagodsky, B. Pesala, C. Chase, W. Hofmann, F. Koyama, and C. J. Chang-Hasnain, “Monolithically integrated multi-wavelength VCSEL arrays using high-contrast gratings,” Opt. Express 18(2), 694–699 (2010).
[CrossRef] [PubMed]

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “A novel ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Opt. Express 17(3), 1508–1517 (2009).
[CrossRef] [PubMed]

C. J. Chang-Hasnain, Y. Zhou, M. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15(3), 869–878 (2009).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high contrast grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Chase, C.

Chavel, P.

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

Clausnitzer, T.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Danzmann, K.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Dhoedt, B.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Fedeli, J.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Forchel, A.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Friedman, D. J.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Friedrich, D.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

Fuchs, H.-J.

Gaylord, T. K.

Geisz, J. F.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Glaser, T.

Goeman, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Green, W. M. J.

Haller, E. E.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Harduin, J.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Hofmann, C.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Hofmann, W.

Huang, M.

C. J. Chang-Hasnain, Y. Zhou, M. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15(3), 869–878 (2009).
[CrossRef]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high contrast grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Hugonin, J. P.

Ishikawa, A.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[CrossRef] [PubMed]

Karagodsky, V.

Keldysh, L. V.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kern, J.

Kley, E. B.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Kley, E.-B.

Koyama, F.

Kuhn, S.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kulakovskii, V. D.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kurtz, S. R.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Lalanne, P.

Launois, H.

Letartre, X.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Li, L.

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40(4), 553–573 (1993).
[CrossRef]

Löffler, A.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Lu, F.

Magnusson, R.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

Mahrt, R. F.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

Moewe, M.

Moharam, M. G.

Moll, N.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Mollenhauer, T.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Nishioka, M.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[CrossRef] [PubMed]

Olivier, N.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Olson, J. M.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Peng, S. T.

Peng, Z.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Pesala, B.

Reinecke, T. L.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Reitzenstein, S.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Rooks, M. J.

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

Scherf, U.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Schnabel, R.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Schröter, S.

Sciancalepore, C.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Seassal, C.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Sedgwick, F. G.

Sek, G.

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Sekaric, L.

Shan, W.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

Stöferle, T.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

Tünnermann, A.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Van Daele, P.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Vandeputte, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

Viktorovitch, P.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Vlasov, Y. A.

Wahlbrink, T.

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Walukiewicz, W.

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

Weisbuch, C.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[CrossRef] [PubMed]

Zhou, Y.

C. J. Chang-Hasnain, Y. Zhou, M. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15(3), 869–878 (2009).
[CrossRef]

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “A novel ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Opt. Express 17(3), 1508–1517 (2009).
[CrossRef] [PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high contrast grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. J. Chang-Hasnain, Y. Zhou, M. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15(3), 869–878 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high contrast grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSELs,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40(4), 553–573 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

T. Stöferle, N. Moll, T. Wahlbrink, J. Bolten, T. Mollenhauer, U. Scherf, and R. F. Mahrt, “Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator,” Nano Lett. 10(9), 3675–3678 (2010).
[CrossRef] [PubMed]

Nat. Photonics (3)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Nature (1)

J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. Lett. (3)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[CrossRef] [PubMed]

W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloy,s,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[CrossRef]

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104(16), 163903 (2010).
[CrossRef] [PubMed]

Other (5)

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (CRC Press, 1997).

B. C. Kress and P. Meyrueis, Applied Digital Optics: from Micro-optics to Nanophotonics (Wiley, 2009)

D. J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

T. Tamir, G. Griffel, and H. L. Bertoni, eds., Guided-Wave Optoelectronics, 2nd ed. (Springer-Verlag, 1990).

B. Pesala, V. Karagodsky and C. Chang-Hasnain, “"Ultra-compact optical coupler and splitter using high-contrast grating hollow-core waveguide," in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper IWH1.

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Figures (4)

Fig. 1
Fig. 1

(a) Basic HCG structure. The grating comprises of simple dielectric bars with high refractive index surrounded by a low index medium. The plane wave is incident from the top in the surface normal direction. The incident plane wave excites waveguide array modes, which propagate downward from z = 0 to z = tg. (b) Examples of two types of extraordinary reflectivity features: broad-band high reflectivity (blue) and high-Q resonances (red). The broadband reflector HCG dimensions are: Λ = 772nm, tg = 502nm, η = 77%, nr = 3.2137 and TM polarized light. The high-Q resonator HCG is TE polarized with Λ = 716nm, tg = 1494nm, η = 70%, nr = 3.48. The spectra were calculated using RCWA. (c) Dispersion curves of the waveguide array modes (blue lines) calculated using analytic solutions: β being the z-wavenumbers. Between the two light lines (red, dashed) the dispersion resembles that of a slab waveguide [29]. However, below the air light line (β<ω/c) there is a discrete set of modes due to subwavelength grating periodicity. ωc2 and ωc3 are the cutoffs of the second and the third modes respectively, and between them the grating operates at a dual-mode regime.

Fig. 2
Fig. 2

(a) Reflectivity contour of a HCG as a function of wavelength and grating thickness simulated by RCWA. The incident wave has a TE polarized, surface-normal incidence, whereas the grating has a duty cycle of 0.7 and a refractive index of 3.48. The mode cutoffs (λc2, λc3, etc.) are marked to clearly illustrate the differences of the three wavelength-regimes: deep-subwavelength, near-wavelength and diffraction. (b) Analytical solutions of Fabry-Perot (FP) resonance conditions of the individual modes (Eq. (3), shown by the blue curves, superimposed on the reflectivity contour in 2(a). Excellent agreement is obtained between the analytic and simulation results. Green curves correspond to the in-phase selection-rule, whereas yellow curves correspond to the π-phase selection-rule, Eq. (4). The insets show examples of an anti-crossing and a crossing between the FP resonance lines (blue curves).

Fig. 3
Fig. 3

Intensity profiles inside the grating calculated using analytical formulation presented in this paper for (a) an anti-crossing (same anti-crossing as in the inset of Fig. 2(b)), showing 107-fold resonant energy buildup, and (b) a crossing (same as in Fig. 2(b)), showing only weak energy buildup. The parameters are (a) λ/Λ = 2.3291, tg/Λ = 0.8415, η = 0.70, nr = 3.48 and (b) λ/Λ = 2.02, tg/Λ = 0.32, η = 0.70, nr = 3.48, all with TE-polarization.

Fig. 4
Fig. 4

Reflectivity contour for the same HCG as in Fig. 2 but with a shallow angle (θ = 85°) incidence. The crossings and anti-crossings are clearly seen.

Equations (5)

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k s tan( k s s/2 )= n bar 2 k a tan( k a a/2 )
β 2 = ( 2π/λ ) 2 k a 2 = ( 2π n bar /λ ) 2 k s 2
ψ n = Δ phase( eigenvalue #n of ρφ )
ψ n =mπ, where m=1,2,...
| Δψ |=| ψ 2 ψ 1 |=lπ, wherel=0,1,2,

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